Why don't you notice sunburn until the next day?

What's happening when the sun is on your skins is that its causing damage in your skin. The Ultra Violet radiation on from the sun is zooming into your skin cells and causing the DNA in your cells to be damaged. This is prompting a lot of emergency reactions to go on in your skin cells. They realise they're damaged and lots of gene expression and signalling pathways get switched on in response to this damage to either patch up the cells that have been damaged by the sun or to kill themselves to protect your body from this damage. This actually takes some time to get going.

At the same time, because you've damaged your skin, there's going to be some kind of immune response going on as well, your body's activating itself to the damage so this is why you're going to go red, get inflammation, and in some really serious cases you'll get skin blistering and swelling but this does all take time. These are biological processes, the sensing of damage is quite quick but actually getting the response going might well take a couple of hours. It's best not to get sunburnt if you want to reduce your risk of skin cancer.